A particle \(P\) is moving in a circle of radius 2 m . At time \(t\) seconds, its velocity is \((t-1)^{2} \mathrm{~m} \mathrm{~s}^{-1}\). At a particular time \(T\) seconds, where \(T>0\), the magnitude of the radial component of the acceleration of \(P\) is \(8 \mathrm{~m} \mathrm{~s}^{-2}\). Find the magnitude of the transverse component of the acceleration of \(P\) at this instant.